Which Value of x Should be Used for Evaluating Limits in Integral?

[frasifrasi]

For the integral from 0 to -sqrt(2)/2
of arcsin(x)/sqrt(1 - x^2)

I let u = arcsin(x) and the integral became the integral of u du.

Now, when I go to evaluate the limits of integration at arcsin(x) ^(2)/2 , there are two possible value of x that will give me the limit of integration in x <= 2pi, which one should I use and did I do anything wrong?

 

[Dick]

$$\int_{0}^{-\frac{\sqrt{2}}{2}}\frac{\tan^{-1}x}{\sqrt{1-x^2}}dx$$

correct?

Question, what is the derivative of Arctanx?

No, the question says arcsin. And arcsin(-sqrt(2)/2) is a definite number, even though sin(u)=-sqrt(2)/2 has multiple solutions. The domain of arcsin is [-1,1] and the range is [-pi/2,pi/2].

 

[frasifrasi]

so, how do i do this? what does the integral evaluate to?


I am getting u^(2)/2...

 

[Dick]

so, how do i do this? what does the integral evaluate to?


I am getting u^(2)/2...

That's fine, or you can write it as (arcsin(x))^2/2. What's arcsin(-sqrt(2)/2)?

 

[frasifrasi]

I guess I have to use the negative of pi/4 for the domain...

 

[rocomath]

No, the question says arcsin. And arcsin(-sqrt(2)/2) is a definite number, even though sin(u)=-sqrt(2)/2 has multiple solutions. The domain of arcsin is [-1,1] and the range is [-pi/2,pi/2].

I deleted that post! Can't believe you were able to quote it. I had just finished working out so I wasn't thinking right :p

 

[Dick]

I deleted that post! Can't believe you were able to quote it. I had just finished working out so I wasn't thinking right :p

Guess I pounced too quickly. Sorry.